Problem: $3bc + 5bd - 5b - 5 = -c - 7$ Solve for $b$.
Solution: Combine constant terms on the right. $3bc + 5bd - 5b - {5} = -c - {7}$ $3bc + 5bd - 5b = -c - {2}$ Notice that all the terms on the left-hand side of the equation have $b$ in them. $3{b}c + 5{b}d - 5{b} = -c - 2$ Factor out the $b$ ${b} \cdot \left( 3c + 5d - 5 \right) = -c - 2$ Isolate the $b$ $b \cdot \left( {3c + 5d - 5} \right) = -c - 2$ $b = \dfrac{ -c - 2 }{ {3c + 5d - 5} }$ We can simplify this by multiplying the top and bottom by $-1$. $b= \dfrac{c + 2}{-3c - 5d + 5}$